On multiterm time-fractional diffusion equations with additional memory

In this work, we investigate the well-posedness and regularity of solutions to an abstract fractional differential equation that incorporates additional memory effects arising from nonlocal-in-time operators. Such equations are of interest because of their relevance in modeling complex phenomena, such as anomalous diffusion and viscoelastic behavior. We reformulate the problem as a perturbation of a parabolic Volterra integral equation. By applying Laplace transform techniques and resolvent estimates, we establish existence, uniqueness, and regularity results under mild assumptions on the underlying operators and memory kernels.